Lucas Mann (Münster)

Abstract: Using Clausen-Scholze’s theory of condensed mathematics, we construct a full 6-functor formalism for p-adic sheaves on rigid-analytic varieties. As a special case of this formalism we obtain Poincaré duality for the étale F_p-cohomology of smooth proper rigid-analytic varieties. By applying the formalism to classifying stacks of p-adic groups, we obtain new insights into the p-adic Langlands program.